Systems and methods for forming and maintaining a high performance FRC

ABSTRACT

Systems and methods that facilitate the formation and maintenance of new High Performance Field Reversed Configurations (FRCs). An FRC system for the High Performance FRC (HPF) includes a central confinement vessel surrounded by two diametrically opposed reversed-field-theta-pinch formation sections and, beyond the formation sections, two divertor chambers to control neutral density and impurity contamination. A magnetic system includes a series of quasi-dc coils axially positioned along the FRC system components, quasi-dc mirror coils between the confinement chamber and the adjacent formation sections, and mirror plugs between the formation sections and the divertors. The formation sections include modular pulsed power formation systems that enable FRCs to be formed in-situ and then accelerated and injected (=static formation) or formed and accelerated simultaneously (=dynamic formation). The FRC system further includes neutral atom beam injectors, a pellet injector, gettering systems, axial plasma guns and flux surface biasing electrodes.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.13/261,901, filed Feb. 25, 2015, which is a national stage entry of PCTApplication No. PCT/US2012/065071, filed Nov. 14, 2012, which claims thebenefit of U.S. Provisional Application No. 61/559,721, filed Nov. 15,2011, and U.S. Provisional Application No. 61/559,154, filed Nov. 14,2011, the disclosures of all of which are fully incorporated herein byreference.

FIELD

The embodiments described herein relate generally to magnetic plasmaconfinement systems and, more particularly, to systems and methods thatfacilitate forming and maintaining Field Reversed Configurations withsuperior stability as well as particle, energy and flux confinement.

BACKGROUND INFORMATION

The Field Reversed Configuration (FRC) belongs to the class of magneticplasma confinement topologies known as compact toroids (CT). It exhibitspredominantly poloidal magnetic fields and possesses zero or smallself-generated toroidal fields (see M. Tuszewski, Nucl. Fusion 28, 2033(1988)). The attractions of such a configuration are its simple geometryfor ease of construction and maintenance, a natural unrestricteddivertor for facilitating energy extraction and ash removal, and veryhigh β (β is the ratio of the average plasma pressure to the averagemagnetic field pressure inside the FRC), i.e., high power density. Thehigh β nature is advantageous for economic operation and for the use ofadvanced, aneutronic fuels such as D-He³ and p-B¹¹.

The traditional method of forming an FRC uses the field-reversed θ-pinchtechnology, producing hot, high-density plasmas (see A. L. Hoffman andJ. T. Slough, Nucl. Fusion 33, 27 (1993)). A variation on this is thetranslation-trapping method in which the plasma created in a theta-pinch“source” is more-or-less immediately ejected out one end into aconfinement chamber. The translating plasmoid is then trapped betweentwo strong mirrors at the ends of the chamber (see, for instance, H.Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191(1995)). Once in the confinement chamber, various heating and currentdrive methods may be applied such as beam injection (neutral orneutralized), rotating magnetic fields, RF or ohmic heating, etc. Thisseparation of source and confinement functions offers key engineeringadvantages for potential future fusion reactors. FRCs have proved to beextremely robust, resilient to dynamic formation, translation, andviolent capture events. Moreover, they show a tendency to assume apreferred plasma state (see e.g. H. Y. Guo, A. L. Hoffman, K. E. Miller,and L. C. Steinhauer, Phys. Rev. Lett. 92, 245001 (2004)). Significantprogress has been made in the last decade developing other FRC formationmethods: merging spheromaks with oppositely-directed helicities (seee.g. Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama, and T. Okazaki, Nucl.Fusion 39, 2001 (1999)) and by driving current with rotating magneticfields (RMF) (see e.g. I. R. Jones, Phys. Plasmas 6, 1950 (1999)) whichalso provides additional stability.

Recently, the collision-merging technique, proposed long ago (see e.g.D. R. Wells, Phys. Fluids 9, 1010 (1966)) has been significantlydeveloped further: two separate theta-pinches at opposite ends of aconfinement chamber simultaneously generate two plasmoids and acceleratethe plasmoids toward each other at high speed; they then collide at thecenter of the confinement chamber and merge to form a compound FRC. Inthe construction and successful operation of one of the largest FRCexperiments to date, the conventional collision-merging method was shownto produce stable, long-lived, high-flux, high temperature FRCs (seee.g. M. Binderbauer, H. Y. Guo, M. Tuszewski et al., Phys. Rev. Lett.105, 045003 (2010)).

FRCs consist of a torus of closed field lines inside a separatrix, andof an annular edge layer on the open field lines just outside theseparatrix. The edge layer coalesces into jets beyond the FRC length,providing a natural divertor. The FRC topology coincides with that of aField-Reversed-Mirror plasma. However, a significant difference is thatthe FRC plasma has a β of about 10. The inherent low internal magneticfield provides for a certain indigenous kinetic particle population,i.e. particles with large larmor radii, comparable to the FRC minorradius. It is these strong kinetic effects that appear to at leastpartially contribute to the gross stability of past and present FRCs,such as those produced in the collision-merging experiment.

Typical past FRC experiments have been dominated by convective losseswith energy confinement largely determined by particle transport.Particles diffuse primarily radially out of the separatrix volume, andare then lost axially in the edge layer. Accordingly, FRC confinementdepends on the properties of both closed and open field line regions.The particle diffusion time out of the separatrix scales asτ_(⊥)˜a²/D_(⊥) (a·r_(s)/4, where r_(s) is the central separatrixradius), and D_(⊥) is a characteristic FRC diffusivity, such asD_(⊥)˜12.5 ρ_(ie), with ρ_(ie) representing the ion gyroradius,evaluated at an externally applied magnetic field. The edge layerparticle confinement time τ_(∥) is essentially an axial transit time inpast FRC experiments. In steady-state, the balance between radial andaxial particle losses yields a separatrix density gradient lengthsδ˜(D_(⊥)τ_(∥))^(1/2). The FRC particle confinement time scales as(τ_(⊥)τ_(∥))^(1/2) for past FRCs that have substantial density at theseparatrix (see e.g. M. Tuszewski, “Field Reversed Configurations,”Nucl. Fusion 28, 2033 (1988)).

Another drawback of prior FRC system designs was the need to useexternal multipoles to control rotational instabilities such as the fastgrowing n=2 interchange instabilities. In this way the typicalexternally applied quadrupole fields provided the required magneticrestoring pressure to dampen the growth of these unstable modes. Whilethis technique is adequate for stability control of the thermal bulkplasma, it poses a severe problem for more kinetic FRCs or advancedhybrid FRCs, where a highly kinetic large orbit particle population iscombined with the usual thermal plasma. In these systems, thedistortions of the axisymmetric magnetic field due to such multipolefields leads to dramatic fast particle losses via collisionlessstochastic diffusion, a consequence of the loss of conservation ofcanonical angular momentum. A novel solution to provide stabilitycontrol without enhancing diffusion of any particles is, thus, importantto take advantage of the higher performance potential of thesenever-before explored advanced FRC concepts.

In light of the foregoing, it is, therefore, desirable to improve theconfinement and stability of FRCs in order to use steady state FRCs as apathway to a whole variety of applications from compact neutron sources(for medical isotope production and nuclear waste remediation), to massseparation and enrichment systems, and to a reactor core for fusion oflight nuclei for the future generation of energy.

SUMMARY

The present embodiments provided herein are directed to systems andmethods that facilitate the formation and maintenance of new HighPerformance Field Reversed Configurations (FRCs). In accordance withthis new High Performance FRC paradigm, the present system combines ahost of novel ideas and means to dramatically improve FRC confinement ofparticles, energy and flux as well as provide stability control withoutnegative side-effects.

An FRC system provided herein includes a central confinement vesselsurrounded by two diametrically opposed reversed-field-theta-pinchformation sections and, beyond the formation sections, two divertorchambers to control neutral density and impurity contamination. Amagnetic system includes a series of quasi-dc coils that are situated ataxial positions along the components of the FRC system, quasi-dc mirrorcoils between either end of the confinement chamber and the adjacentformation sections, and mirror plugs comprising compact quasi-dc mirrorcoils between each of the formation sections and divertors that produceadditional guide fields to focus the magnetic flux surfaces towards thedivertor. The formation sections include modular pulsed power formationsystems that enable FRCs to be formed in-situ and then accelerated andinjected (=static formation) or formed and accelerated simultaneously(=dynamic formation).

The FRC system includes neutral atom beam injectors and a pelletinjector. Gettering systems are also included as well as axial plasmaguns. Biasing electrodes are also provided for electrical biasing ofopen flux surfaces.

The systems, methods, features and advantages of the invention will beor will become apparent to one with skill in the art upon examination ofthe following figures and detailed description. It is intended that allsuch additional methods, features and advantages be included within thisdescription, be within the scope of the invention, and be protected bythe accompanying claims. It is also intended that the invention is notlimited to require the details of the example embodiments.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying drawings, which are included as part of the presentspecification, illustrate the presently preferred embodiment and,together with the general description given above and the detaileddescription of the preferred embodiment given below, serve to explainand teach the principles of the present invention.

FIG. 1 illustrates particle confinement in the present FRC system undera high performance FRC regime (HPF) versus under a conventional FRCregime (CR), and versus other conventional FRC experiments.

FIG. 2 illustrates the components of the present FRC system and themagnetic topology of an FRC producible in the present FRC system.

FIG. 3 illustrates the basic layout of the present FRC system as viewedfrom the top, including the preferred arrangement of neutral beams,electrodes, plasma guns, mirror plugs and pellet injector.

FIG. 4 illustrates a schematic of the components of a pulsed powersystem for the formation sections.

FIG. 5 illustrates an isometric view of an individual pulsed powerformation skid.

FIG. 6 illustrates an isometric view of a formation tube assembly.

FIG. 7 illustrates a partial sectional isometric view of neutral beamsystem and key components.

FIG. 8 illustrates an isometric view of the neutral beam arrangement onconfinement chamber.

FIG. 9 illustrates a partial sectional isometric view of a preferredarrangement of the Ti and Li gettering systems.

FIG. 10 illustrates a partial sectional isometric view of a plasma guninstalled in the divertor chamber. Also shown are the associatedmagnetic mirror plug and a divertor electrode assembly.

FIG. 11 illustrates a preferred layout of an annular bias electrode atthe axial end of the confinement chamber.

FIG. 12 illustrates the evolution of the excluded flux radius in the FRCsystem obtained from a series of external diamagnetic loops at the twofield reversed theta pinch formation sections and magnetic probesembedded inside the central metal confinement chamber. Time is measuredfrom the instant of synchronized field reversal in the formationsources, and distance z is given relative to the axial midplane of themachine.

FIGS. 13A, 13B, 13C, and 13D illustrate data from a representativenon-HPF, un-sustained discharge on the present FRC system. Shown asfunctions of time are (FIG. 13A) excluded flux radius at the midplane,(FIG. 13B) 6 chords of line-integrated density from the midplane CO2interferometer, (FIG. 13C) Abel-inverted density radial profiles fromthe CO2 interferometer data, and (FIG. 13D) total plasma temperaturefrom pressure balance.

FIG. 14 illustrates the excluded flux axial profiles at selected timesfor the same discharge of the present FRC system shown in FIGS. 13A,13B, 13C and 13D.

FIG. 15 illustrates an isometric view of the saddle coils mountedoutside of the confinement chamber.

FIGS. 16A, 16B, 16C and 16D illustrate the correlations of FRC lifetimeand pulse length of injected neutral beams. As shown, longer beam pulsesproduce longer lived FRCs.

FIGS. 17A, 17B, 17C and 17D illustrate the individual and combinedeffects of different components of the FRC system on FRC performance andthe attainment of the HPF regime.

FIGS. 18A, 18B, 18C and 18D illustrate data from a representative HPF,un-sustained discharge on the present FRC system. Shown as functions oftime are (FIG. 18A) excluded flux radius at the midplane, (FIG. 18B) 6chords of line-integrated density from the midplane CO2 interferometer,(FIG. 18C) Abel-inverted density radial profiles from the CO2interferometer data, and (FIG. 18D) total plasma temperature frompressure balance.

FIG. 19 illustrates flux confinement as a function of electrontemperature (T_(e)). It represents a graphical representation of a newlyestablished superior scaling regime for HPF discharges.

It should be noted that the figures are not necessarily drawn to scaleand that elements of similar structures or functions are generallyrepresented by like reference numerals for illustrative purposesthroughout the figures. It also should be noted that the figures areonly intended to facilitate the description of the various embodimentsdescribed herein. The figures do not necessarily describe every aspectof the teachings disclosed herein and do not limit the scope of theclaims.

DETAILED DESCRIPTION

The present embodiments provided herein are directed to systems andmethods that facilitate forming and maintaining High Performance FieldReversed Configurations (FRCs) with superior stability as well assuperior particle, energy and flux confinement over conventional FRCs.Various ancillary systems and operating modes have been explored toassess whether there is a superior confinement regime in FRCs. Theseefforts have led to breakthrough discoveries and the development of aHigh Performance FRC paradigm described herein. In accordance with thisnew paradigm, the present systems and methods combine a host of novelideas and means to dramatically improve FRC confinement as illustratedin FIG. 1 as well as provide stability control without negativeside-effects. As discussed in greater detail below, FIG. 1 depictsparticle confinement in an FRC system 10 described below (see FIGS. 2and 3), operating in accordance a High Performance FRC regime (HPF) forforming and maintaining an FRC versus operating in accordance with aconventional regime CR for forming and maintaining an FRC, and versusparticle confinement in accordance with conventional regimes for formingand maintaining an FRC used in other experiments. The present disclosurewill outline and detail the innovative individual components of the FRCsystem 10 and methods as well as their collective effects.

Description of the FRC System

Vacuum System

FIGS. 2 and 3 depict a schematic of the present FRC system 10. The FRCsystem 10 includes a central confinement vessel 100 surrounded by twodiametrically opposed reversed-field-theta-pinch formation sections 200and, beyond the formation sections 200, two divertor chambers 300 tocontrol neutral density and impurity contamination. The present FRCsystem 10 was built to accommodate ultrahigh vacuum and operates attypical base pressures of 10-8 torr. Such vacuum pressures require theuse of double-pumped mating flanges between mating components, metalO-rings, high purity interior walls, as well as careful initial surfaceconditioning of all parts prior to assembly, such as physical andchemical cleaning followed by 24 hour 250° C. vacuum baking and Hydrogenglow discharge cleaning.

The reversed-field-theta-pinch formation sections 200 are standardfield-reversed-theta-pinches (FRTPs), albeit with an advanced pulsedpower formation system discussed in detail below (see FIGS. 4 through6). Each formation section 200 is made of standard opaque industrialgrade quartz tubes that feature a 2 millimeter inner lining of ultrapurequartz. The confinement chamber 100 is made of stainless steel to allowa multitude of radial and tangential ports; it also serves as a fluxconserver on the timescale of the experiments described below and limitsfast magnetic transients. Vacuums are created and maintained within theFRC system 10 with a set of dry scroll roughing pumps, turbo molecularpumps and cryo pumps.

Magnetic System

The magnetic system 400 is illustrated in FIGS. 2 and 3. FIG. 2, amongstother features, illustrates an FRC magnetic flux and density contours(as functions of the radial and axial coordinates) pertaining to an FRC450 producible by the FRC system 10. These contours were obtained by a2-D resistive Hall-MHD numerical simulation using code developed tosimulate systems and methods corresponding to the FRC system 10, andagree well with measured experimental data. As seen in FIG. 2, the FRC450 consists of a torus of closed field lines at the interior 453 of theFRC 450 inside a separatrix 451, and of an annular edge layer 456 on theopen field lines 452 just outside the separatrix 451. The edge layer 456coalesces into jets 454 beyond the FRC length, providing a naturaldivertor.

The main magnetic system 410 includes a series of quasi-dc coils 412,414, and 416 that are situated at particular axial positions along thecomponents, i.e., along the confinement chamber 100, the formationsections 200 and the divertors 300, of the FRC system 10. The quasi-dccoils 412, 414 and 416 are fed by quasi-dc switching power supplies andproduce basic magnetic bias fields of about 0.1 T in the confinementchamber 100, the formation sections 200 and the divertors 300. Inaddition to the quasi-dc coils 412, 414 and 416, the main magneticsystem 410 includes quasi-dc mirror coils 420 (fed by switchingsupplies) between either end of the confinement chamber 100 and theadjacent formation sections 200. The quasi-dc mirror coils 420 providemagnetic mirror ratios of up to 5 and can be independently energized forequilibrium shaping control. In addition, mirror plugs 440, arepositioned between each of the formation sections 200 and divertors 300.The mirror plugs 440 comprise compact quasi-dc mirror coils 430 andmirror plug coils 444. The quasi-dc mirror coils 430 include three coils432, 434 and 436 (fed by switching supplies) that produce additionalguide fields to focus the magnetic flux surfaces 455 towards the smalldiameter passage 442 passing through the mirror plug coils 444. Themirror plug coils 444, which wrap around the small diameter passage 442and are fed by LC pulsed power circuitry, produce strong magnetic mirrorfields of up to 4 T. The purpose of this entire coil arrangement is totightly bundle and guide the magnetic flux surfaces 455 andend-streaming plasma jets 454 into the remote chambers 310 of thedivertors 300. Finally, a set of saddle-coil “antennas” 460 (see FIG.15) are located outside the confinement chamber 100, two on each side ofthe mid-plane, and are fed by dc power supplies. The saddle-coilantennas 460 can be configured to provide a quasi-static magnetic dipoleor quadrupole field of about 0.01 T for controlling rotationalinstabilities and/or electron current control. The saddle-coil antennas460 can flexibly provide magnetic fields that are either symmetric orantisymmetric about the machine's midplane, depending on the directionof the applied currents.

Pulsed Power Formation Systems

The pulsed power formation systems 210 operate on a modified theta-pinchprinciple. There are two systems that each power one of the formationsections 200. FIGS. 4 through 6 illustrate the main building blocks andarrangement of the formation systems 210. The formation system 210 iscomposed of a modular pulsed power arrangement that consists ofindividual units (=skids) 220 that each energize a sub-set of coils 232of a strap assembly 230 (=straps) that wrap around the formation quartztubes 240. Each skid 220 is composed of capacitors 221, inductors 223,fast high current switches 225 and associated trigger 222 and dumpcircuitry 224. In total, each formation system 210 stores between350-400 kJ of capacitive energy, which provides up to 35 GW of power toform and accelerate the FRCs. Coordinated operation of these componentsis achieved via a state-of-the-art trigger and control system 222 and224 that allows synchronized timing between the formation systems 210 oneach formation section 200 and minimizes switching jitter to tens ofnanoseconds. The advantage of this modular design is its flexibleoperation: FRCs can be formed in-situ and then accelerated and injected(=static formation) or formed and accelerated at the same time (=dynamicformation).

Neutral Beam Injectors

Neutral atom beams are deployed on the FRC system 10 to provide heatingand current drive as well as to develop fast particle pressure. As shownin FIGS. 3 and 8, the individual beam lines comprising neutral atom beaminjector systems 610 and 640 are located around the central confinementchamber 100 and inject fast particles tangentially to the FRC plasma(and perpendicular to the axis of the confinement chamber 100) with animpact parameter such that the target trapping zone lies well within theseparatrix 451 (see FIG. 2). Each injector system 610 and 640 is capableof projecting up to 1 MW of neutral beam power into the FRC plasma withparticle energies between 20 and 40 keV. The systems 610 and 640 arebased on positive ion multi-aperture extraction sources and utilizegeometric focusing, inertial cooling of the ion extraction grids anddifferential pumping. Apart from using different plasma sources, thesystems 610 and 640 are primarily differentiated by their physicaldesign to meet their respective mounting locations, yielding side andtop injection capabilities. Typical components of these neutral beaminjectors are specifically illustrated in FIG. 7 for the side injectorsystems 610. As shown in FIG. 7, each individual neutral beam system 610includes an RF plasma source 612 at an input end (this is substitutedwith an arc source in systems 640) with a magnetic screen 614 coveringthe end. An ion optical source and acceleration grids 616 is coupled tothe plasma source 612 and a gate valve 620 is positioned between the ionoptical source and acceleration grids 616 and a neutralizer 622. Adeflection magnet 624 and an ion dump 628 are located between theneutralizer 622 and an aiming device 630 at the exit end. A coolingsystem comprises two cryo-refrigerators 634, two cryopanels 636 and aLN2 shroud 638. This flexible design allows for operation over a broadrange of FRC parameters.

Pellet Injector

To provide a means to inject new particles and better control FRCparticle inventory, a 12-barrel pellet injector 700 (see e.g. I. Vinyaret al., “Pellet Injectors Developed at PELIN for JET, TAE, and HL-2A,”Proceedings of the 26th Fusion Science and Technology Symposium, 09/27to 10/01 (2010)) is utilized on FRC system 10. FIG. 3 illustrates thelayout of the pellet injector 700 on the FRC system 10. The cylindricalpellets (D˜1 mm, L˜1-2 mm) are injected into the FRC with a velocity inthe range of 150-250 km/s. Each individual pellet contains about 5×10¹⁹hydrogen atoms, which is comparable to the FRC particle inventory.

Gettering Systems

It is well known that neutral halo gas is a serious problem in allconfinement systems. The charge exchange and recycling (release of coldimpurity material from the wall) processes can have a devastating effecton energy and particle confinement. In addition, any significant densityof neutral gas at or near the edge will lead to prompt losses of or atleast severely curtail the lifetime of injected large orbit (highenergy) particles (large orbit refers to particles having orbits on thescale of the FRC topology or at least orbit radii much larger than thecharacteristic magnetic field gradient length scale)—a fact that isdetrimental to all energetic plasma applications, including fusion viaauxiliary beam heating.

Surface conditioning is a means by which the detrimental effects ofneutral gas and impurities can be controlled or reduced in a confinementsystem. To this end the FRC system 10 provided herein employs Titaniumand Lithium deposition systems 810 and 820 that coat the plasma facingsurfaces of the confinement chamber (or vessel) 100 and diverters 300with films (tens of micrometers thick) of Ti and/or Li. The coatings areachieved via vapor deposition techniques. Solid Li and/or Ti areevaporated and/or sublimated and sprayed onto nearby surfaces to formthe coatings. The sources are atomic ovens with guide nozzles (in caseof Li) 822 or heated spheres of solid with guide shrouding (in case ofTi) 812. Li evaporator systems typically operate in a continuous modewhile Ti sublimators are mostly operated intermittently in betweenplasma operation. Operating temperatures of these systems are above 600°C. to obtain fast deposition rates. To achieve good wall coverage,multiple strategically located evaporator/sublimator systems arenecessary. FIG. 9 details a preferred arrangement of the getteringdeposition systems 810 and 820 in the FRC system 10. The coatings act asgettering surfaces and effectively pump atomic and molecular hydrogenicspecies (H and D). The coatings also reduce other typical impuritiessuch as Carbon and Oxygen to insignificant levels.

Mirror Plugs

As stated above, the FRC system 10 employs sets of mirror coils 420,430, and 444 as shown in FIGS. 2 and 3. A first set of mirror coils 420is located at the two axial ends of the confinement chamber 100 and isindependently energized from the confinement coils 412, 414 and 416 ofthe main magnetic system 410. The first set of mirror coils 420primarily helps to steer and axially contain the FRC 450 during mergingand provides equilibrium shaping control during sustainment. The firstmirror coil set 420 produces nominally higher magnetic fields (around0.4 to 0.5 T) than the central confinement field produced by the centralconfinement coils 412. The second set of mirror coils 430, whichincludes three compact quasi-dc mirror coils 432, 434 and 436, islocated between the formation sections 200 and the divertors 300 and aredriven by a common switching power supply. The mirror coils 432, 434 and436, together with the more compact pulsed mirror plug coils 444 (fed bya capacitive power supply) and the physical constriction 442 form themirror plugs 440 that provide a narrow low gas conductance path withvery high magnetic fields (between 2 to 4 T with risetimes of about 10to 20 ms). The most compact pulsed mirror coils 444 are of compactradial dimensions, bore of 20 cm and similar length, compared to themeter-plus-scale bore and pancake design of the confinement coils 412,414 and 416. The purpose of the mirror plugs 440 is multifold: (1) Thecoils 432, 434, 436 and 444 tightly bundle and guide the magnetic fluxsurfaces 452 and end-streaming plasma jets 454 into the remote divertorchambers 300. This assures that the exhaust particles reach thedivertors 300 appropriately and that there are continuous flux surfaces455 that trace from the open field line 452 region of the central FRC450 all the way to the divertors 300. (2) The physical constrictions 442in the FRC system 10, through which that the coils 432, 434, 436 and 444enable passage of the magnetic flux surfaces 452 and plasma jets 454,provide an impediment to neutral gas flow from the plasma guns 350 thatsit in the divertors 300. In the same vein, the constrictions 442prevent back-streaming of gas from the formation sections 200 to thedivertors 300 thereby reducing the number of neutral particles that hasto be introduced into the entire FRC system 10 when commencing the startup of an FRC. (3) The strong axial mirrors produced by the coils 432,434, 436 and 444 reduce axial particle losses and thereby reduce theparallel particle diffusivity on open field lines.

Axial Plasma Guns

Plasma streams from guns 350 mounted in the divertor chambers 310 of thedivertors 300 are intended to improve stability and neutral beamperformance. The guns 350 are mounted on axis inside the chamber 310 ofthe divertors 300 as illustrated in FIGS. 3 and 10 and produce plasmaflowing along the open flux lines 452 in the divertor 300 and towardsthe center of the confinement chamber 100. The guns 350 operate at ahigh density gas discharge in a washer-stack channel and are designed togenerate several kiloamperes of fully ionized plasma for 5 to 10 ms. Theguns 350 include a pulsed magnetic coil that matches the output plasmastream with the desired size of the plasma in the confinement chamber100. The technical parameters of the guns 350 are characterized by achannel having a 5 to 13 cm outer diameter and up to about 10 cm innerdiameter and provide a discharge current of 10-15 kA at 400-600 V with agun-internal magnetic field of between 0.5 to 2.3 T.

The gun plasma streams can penetrate the magnetic fields of the mirrorplugs 440 and flow into the formation section 200 and confinementchamber 100. The efficiency of plasma transfer through the mirror plug440 increases with decreasing distance between the gun 350 and the plug440 and by making the plug 440 wider and shorter. Under reasonableconditions, the guns 350 can each deliver approximately 10²² protons/sthrough the 2 to 4 T mirror plugs 440 with high ion and electrontemperatures of about 150 to 300 eV and about 40 to 50 eV, respectively.The guns 350 provide significant refueling of the FRC edge layer 456,and an improved overall FRC particle confinement.

To further increase the plasma density, a gas box could be utilized topuff additional gas into the plasma stream from the guns 350. Thistechnique allows a several-fold increase in the injected plasma density.In the FRC system 10, a gas box installed on the divertor 300 side ofthe mirror plugs 440 improves the refueling of the FRC edge layer 456,formation of the FRC 450, and plasma line-tying.

Given all the adjustment parameters discussed above and also taking intoaccount that operation with just one or both guns is possible, it isreadily apparent that a wide spectrum of operating modes is accessible.

Biasing Electrodes

Electrical biasing of open flux surfaces can provide radial potentialsthat give rise to azimuthal E×B motion that provides a controlmechanism, analogous to turning a knob, to control rotation of the openfield line plasma as well as the actual FRC core 450 via velocity shear.To accomplish this control, the FRC system 10 employs various electrodesstrategically placed in various parts of the machine. FIG. 3 depictsbiasing electrodes positioned at preferred locations within the FRCsystem 10.

In principle, there are 4 classes of electrodes: (1) point electrodes905 in the confinement chamber 100 that make contact with particularopen field lines 452 in the edge of the FRC 450 to provide localcharging, (2) annular electrodes 900 between the confinement chamber 100and the formation sections 200 to charge far-edge flux layers 456 in anazimuthally symmetric fashion, (3) stacks of concentric electrodes 910in the divertors 300 to charge multiple concentric flux layers 455(whereby the selection of layers is controllable by adjusting coils 416to adjust the divertor magnetic field so as to terminate the desiredflux layers 456 on the appropriate electrodes 910), and finally (4) theanodes 920 (see FIG. 10) of the plasma guns 350 themselves (whichintercept inner open flux surfaces 455 near the separatrix of the FRC450). FIGS. 10 and 11 show some typical designs for some of these.

In all cases these electrodes are driven by pulsed or dc power sourcesat voltages up to about 800 V. Depending on electrode size and what fluxsurfaces are intersected, currents can be drawn in the kilo-ampererange.

Un-Sustained Operation of FRC System—Conventional Regime

The standard plasma formation on the FRC system 10 follows thewell-developed reversed-field-theta-pinch technique. A typical processfor starting up an FRC commences by driving the quasi-dc coils 412, 414,416, 420, 432, 434 and 436 to steady state operation. The RFTP pulsedpower circuits of the pulsed power formation systems 210 then drive thepulsed fast reversed magnet field coils 232 to create a temporaryreversed bias of about −0.05 T in the formation sections 200. At thispoint a predetermined amount of neutral gas at 9-20 psi is injected intothe two formation volumes defined by the quartz-tube chambers 240 of the(north and south) formation sections 200 via a set ofazimuthally-oriented puff-vales at flanges located on the outer ends ofthe formation sections 200. Next a small RF (˜hundreds of kilo-hertz)field is generated from a set of antennas on the surface of the quartztubes 240 to create pre-pre-ionization in the form of local seedionization regions within the neutral gas columns. This is followed byapplying a theta-ringing modulation on the current driving the pulsedfast reversed magnet field coils 232, which leads to more globalpre-ionization of the gas columns. Finally, the main pulsed power banksof the pulsed power formation systems 210 are fired to drive pulsed fastreversed magnet field coils 232 to create a forward-biased field of upto 0.4 T. This step can be time-sequenced such that the forward-biasedfield is generated uniformly throughout the length of the formationtubes 240 (static formation) or such that a consecutive peristalticfield modulation is achieved along the axis of the formation tubes 240(dynamic formation).

In this entire formation process, the actual field reversal in theplasma occurs rapidly, within about 5 μs. The multi-gigawatt pulsedpower delivered to the forming plasma readily produces hot FRCs whichare then ejected from the formation sections 200 via application ofeither a time-sequenced modulation of the forward magnetic field(magnetic peristalsis) or temporarily increased currents in the lastcoils of coil sets 232 near the axial outer ends of the formation tubes210 (forming an axial magnetic field gradient that points axiallytowards the confinement chamber 100). The two (north and south)formation FRCs so formed and accelerated then expand into the largerdiameter confinement chamber 100, where the quasi-dc coils 412 produce aforward-biased field to control radial expansion and provide theequilibrium external magnetic flux.

Once the north and south formation FRCs arrive near the midplane of theconfinement chamber 100, the FRCs collide. During the collision theaxial kinetic energies of the north and south formation FRCs are largelythermalized as the FRCs merge ultimately into a single FRC 450. A largeset of plasma diagnostics are available in the confinement chamber 100to study the equilibria of the FRC 450. Typical operating conditions inthe FRC system 10 produce compound FRCs with separatrix radii of about0.4 m and about 3 m axial extend. Further characteristics are externalmagnetic fields of about 0.1 T, plasma densities around 5×10¹⁹ m⁻³ andtotal plasma temperature of up to 1 keV. Without any sustainment, i.e.,no heating and/or current drive via neutral beam injection or otherauxiliary means, the lifetime of these FRCs is limited to about 1 ms,the indigenous characteristic configuration decay time.

Experimental Data of Unsustained Operation—Conventional Regime

FIG. 12 shows a typical time evolution of the excluded flux radius,r_(ΔΦ), which approximates the separatrix radius, r_(S), to illustratethe dynamics of the theta-pinch merging process of the FRC 450. The two(north and south) individual plasmoids are produced simultaneously andthen accelerated out of the respective formation sections 200 at asupersonic speed, v_(Z)˜250 km/s, and collide near the midplane at z=0.During the collision the plasmoids compress axially, followed by a rapidradial and axial expansion, before eventually merging to form an FRC450. Both radial and axial dynamics of the merging FRC 450 are evidencedby detailed density profile measurements and bolometer-based tomography.

Data from a representative un-sustained discharge of the FRC system 10are shown as functions of time in FIGS. 13A, 13B, 13C, and 13D. The FRCis initiated at t=0. The excluded flux radius at the machine's axialmid-plane is shown in FIG. 13A. This data is obtained from an array ofmagnetic probes, located just inside the confinement chamber's stainlesssteel wall, that measure the axial magnetic field. The steel wall is agood flux conserver on the time scales of this discharge.

Line-integrated densities are shown in FIG. 13B, from a 6-chordCO₂/He—Ne interferometer located at z=0. Taking into account vertical(y) FRC displacement, as measured by bolometric tomography, Abelinversion yields the density contours of FIG. 13C. After some axial andradial sloshing during the first 0.1 ms, the FRC settles with a hollowdensity profile. This profile is fairly flat, with substantial densityon axis, as required by typical 2-D FRC equilibria.

Total plasma temperature is shown in FIG. 13D, derived from pressurebalance and fully consistent with Thomson scattering and spectroscopymeasurements.

Analysis from the entire excluded flux array indicates that the shape ofthe FRC separatrix (approximated by the excluded flux axial profiles)evolves gradually from racetrack to elliptical. This evolution, shown inFIG. 14, is consistent with a gradual magnetic reconnection from two toa single FRC. Indeed, rough estimates suggest that in this particularinstant about 10% of the two initial FRC magnetic fluxes reconnectsduring the collision.

The FRC length shrinks steadily from 3 down to about 1 m during the FRClifetime. This shrinkage, visible in FIG. 14, suggests that mostlyconvective energy loss dominates the FRC confinement. As the plasmapressure inside the separatrix decreases faster than the externalmagnetic pressure, the magnetic field line tension in the end regionscompresses the FRC axially, restoring axial and radial equilibrium. Forthe discharge discussed in FIGS. 13A, 13B, 13C, 13D and 14, the FRCmagnetic flux, particle inventory, and thermal energy (about 10 mWb,7×10¹⁹ particles, and 7 kJ, respectively) decrease by roughly an orderof magnitude in the first millisecond, when the FRC equilibrium appearsto subside.

Sustained Operation—HPF Regime

The examples in FIGS. 12 to 14 are characteristic of decaying FRCswithout any sustainment. However, several techniques are deployed on theFRC system 10 to further improve FRC confinement (inner core and edgelayer) to the HPF regime and sustain the configuration.

Neutral Beams

First, fast (H) neutrals are injected perpendicular to B_(Z) in beamsfrom the eight neutral beam injectors 600. The beams of fast neutralsare injected from the moment the north and south formation FRCs merge inthe confinement chamber 100 into one FRC 450. The fast ions, createdprimarily by charge exchange, have betatron orbits (with primary radiion the scale of the FRC topology or at least much larger than thecharacteristic magnetic field gradient length scale) that add to theazimuthal current of the FRC 450. After some fraction of the discharge(after 0.5 to 0.8 ms into the shot), a sufficiently large fast ionpopulation significantly improves the inner FRC's stability andconfinement properties (see e.g. M. W. Binderbauer and N. Rostoker,Plasma Phys. 56, part 3, 451 (1996)). Furthermore, from a sustainmentperspective, the beams from the neutral beam injectors 600 are also theprimary means to drive current and heat the FRC plasma.

In the plasma regime of the FRC system 10, the fast ions slow downprimarily on plasma electrons. During the early part of a discharge,typical orbit-averaged slowing-down times of fast ions are 0.3-0.5 ms,which results in significant FRC heating, primarily of electrons. Thefast ions make large radial excursions outside of the separatrix becausethe internal FRC magnetic field is inherently low (about 0.03 T onaverage for a 0.1 T external axial field). The fast ions would bevulnerable to charge exchange loss, if the neutral gas density were toohigh outside of the separatrix. Therefore, wall gettering and othertechniques (such as the plasma gun 350 and mirror plugs 440 thatcontribute, amongst other things, to gas control) deployed on the FRCsystem 10 tend to minimize edge neutrals and enable the requiredbuild-up of fast ion current.

Pellet Injection

When a significant fast ion population is built up within the FRC 450,with higher electron temperatures and longer FRC lifetimes, frozen H orD pellets are injected into the FRC 450 from the pellet injector 700 tosustain the FRC particle inventory of the FRC 450. The anticipatedablation timescales are sufficiently short to provide a significant FRCparticle source. This rate can also be increased by enlarging thesurface area of the injected piece by breaking the individual pelletinto smaller fragments while in the barrels or injection tubes of thepellet injector 700 and before entering the confinement chamber 100, astep that can be achieved by increasing the friction between the pelletand the walls of the injection tube by tightening the bend radius of thelast segment of the injection tube right before entry into theconfinement chamber 100. By virtue of varying the firing sequence andrate of the 12 barrels (injection tubes) as well as the fragmentation,it is possible to tune the pellet injection system 700 to provide justthe desired level of particle inventory sustainment. In turn, this helpsmaintain the internal kinetic pressure in the FRC 450 and sustainedoperation and lifetime of the FRC 450.

Once the ablated atoms encounter significant plasma in the FRC 450, theybecome fully ionized. The resultant cold plasma component is thencollisionally heated by the indigenous FRC plasma. The energy necessaryto maintain a desired FRC temperature is ultimately supplied by the beaminjectors 600. In this sense the pellet injectors 700 together with theneutral beam injectors 600 form the system that maintains a steady stateand sustains the FRC 450.

Saddle Coils

To achieve steady state current drive and maintain the required ioncurrent it is desirable to prevent or significantly reduce electron spinup due to the electron-ion frictional force (resulting from collisionalion electron momentum transfer). The FRC system 10 utilizes aninnovative technique to provide electron breaking via an externallyapplied static magnetic dipole or quadrupole field. This is accomplishedvia the external saddle coils 460 depicted in FIG. 15. The transverseapplied radial magnetic field from the saddle coils 460 induces an axialelectric field in the rotating FRC plasma. The resultant axial electroncurrent interacts with the radial magnetic field to produce an azimuthalbreaking force on the electrons, F_(θ)=−σV_(eθ)<|B_(r)|²>. For typicalconditions in the FRC system 10, the required applied magnetic dipole(or quadrupole) field inside the plasma needs to be only of order 0.001T to provide adequate electron breaking. The corresponding externalfield of about 0.015 T is small enough to not cause appreciable fastparticle losses or otherwise negatively impact confinement. In fact, theapplied magnetic dipole (or quadrupole) field contributes to suppressinstabilities. In combination with tangential neutral beam injection andaxial plasma injection, the saddle coils 460 provide an additional levelof control with regards to current maintenance and stability.

Mirror Plugs

The design of the pulsed coils 444 within the mirror plugs 440 permitsthe local generation of high magnetic fields (2 to 4 T) with modest(about 100 kJ) capacitive energy. For formation of magnetic fieldstypical of the present operation of the FRC system 10, all field lineswithin the formation volume are passing through the constrictions 442 atthe mirror plugs 440, as suggested by the magnetic field lines in FIG. 2and plasma wall contact does not occur. Furthermore, the mirror plugs440 in tandem with the quasi-dc divertor magnets 416 can be adjusted soto guide the field lines onto the divertor electrodes 910, or flare thefield lines in an end cusp configuration (not shown). The latterimproves stability and suppresses parallel electron thermal conduction.

The mirror plugs 440 by themselves also contribute to neutral gascontrol. The mirror plugs 440 permit a better utilization of thedeuterium gas puffed in to the quartz tubes during FRC formation, as gasback-streaming into the divertors 300 is significantly reduced by thesmall gas conductance of the plugs (a meager 500 L/s). Most of theresidual puffed gas inside the formation tubes 210 is quickly ionized.In addition, the high-density plasma flowing through the mirror plugs440 provides efficient neutral ionization hence an effective gasbarrier. As a result, most of the neutrals recycled in the divertors 300from the FRC edge layer 456 do not return to the confinement chamber100. In addition, the neutrals associated with the operation of theplasma guns 350 (as discussed below) will be mostly confined to thedivertors 300.

Finally, the mirror plugs 440 tend to improve the FRC edge layerconfinement. With mirror ratios (plug/confinement magnetic fields) inthe range 20 to 40, and with a 15 m length between the north and southmirror plugs 440, the edge layer particle confinement time τ_(∥)increases by up to an order of magnitude. Improving τ_(∥) readilyincreases the FRC particle confinement.

Assuming radial diffusive (D) particle loss from the separatrix volume453 balanced by axial loss (τ_(∥)) from the edge layer 456, one obtains(2πr_(s)L_(s))(Dn_(s)/δ)=(2πr_(s)L_(s)δ)(n_(s)/τ_(∥)), from which theseparatrix density gradient length can be rewritten as δ=(Dτ_(∥))^(1/2).Here r_(s), L_(s) and n_(s) are separatrix radius, separatrix length andseparatrix density, respectively. The FRC particle confinement time isτ_(N)=[πr_(s)²L_(s)<n>]/[(2πr_(s)L_(s))(Dn_(s)/δ)]=(<n>/n_(s))(τ_(⊥)τ_(∥))^(1/2),where τ_(⊥)=a²/D with a=r_(s)/4. Physically, improving τ_(∥) leads toincreased δ (reduced separatrix density gradient and drift parameter),and, therefore, reduced FRC particle loss. The overall improvement inFRC particle confinement is generally somewhat less than quadraticbecause n_(s) increases with τ_(∥).

A significant improvement in τ_(∥) also requires that the edge layer 456remains grossly stable (i.e., no n=1 flute, firehose, or other MHDinstability typical of open systems). Use of the plasma guns 350provides for this preferred edge stability. In this sense, the mirrorplugs 440 and plasma gun 350 form an effective edge control system.

Plasma Guns

The plasma guns 350 improve the stability of the FRC exhaust jets 454 byline-tying. The gun plasmas from the plasma guns 350 are generatedwithout azimuthal angular momentum, which proves useful in controllingFRC rotational instabilities. As such the guns 350 are an effectivemeans to control FRC stability without the need for the older quadrupolestabilization technique. As a result, the plasma guns 350 make itpossible to take advantage of the beneficial effects of fast particlesor access the advanced hybrid kinetic FRC regime as outlined in thisdisclosure. Therefore, the plasma guns 350 enable the FRC system 10 tobe operated with saddle coil currents just adequate for electronbreaking but below the threshold that would cause FRC instability and/orlead to dramatic fast particle diffusion.

As mentioned in the Mirror Plug discussion above, if τ_(∥) can besignificantly improved, the supplied gun plasma would be comparable tothe edge layer particle loss rate (˜10²²/s). The lifetime of thegun-produced plasma in the FRC system 10 is in the millisecond range.Indeed, consider the gun plasma with density n_(e)˜10¹³ cm⁻³ and iontemperature of about 200 eV, confined between the end mirror plugs 440.The trap length L and mirror ratio R are about 15 m and 20,respectively. The ion mean free path due to Coulomb collisions isλ_(ii)˜6×10³ cm and, since λ_(ii) ln R/R<L, the ions are confined in thegas-dynamic regime. The plasma confinement time in this regime isτ_(gd)˜RL/2V_(s)˜2 ms, where V_(s) is the ion sound speed. Forcomparison, the classical ion confinement time for these plasmaparameters would be τ_(c)˜0.5τ_(ii)(ln R+(ln R)^(0.5))˜0.7 ms. Theanomalous transverse diffusion may, in principle, shorten the plasmaconfinement time. However, in the FRC system 10, if we assume the Bohmdiffusion rate, the estimated transverse confinement time for the gunplasma is τ_(⊥)>τ_(gd)˜2 ms. Hence, the guns would provide significantrefueling of the FRC edge layer 456, and an improved overall FRCparticle confinement.

Furthermore, the gun plasma streams can be turned on in about 150 to 200microseconds, which permits use in FRC start-up, translation, andmerging into the confinement chamber 100. If turned on around t˜0 (FRCmain bank initiation), the gun plasmas help to sustain the presentdynamically formed and merged FRC 450. The combined particle inventoriesfrom the formation FRCs and from the guns is adequate for neutral beamcapture, plasma heating, and long sustainment. If turned on at t in therange −1 to 0 ms, the gun plasmas can fill the quartz tubes 210 withplasma or ionize the gas puffed into the quartz tubes, thus permittingFRC formation with reduced or even perhaps zero puffed gas. The lattermay require sufficiently cold formation plasma to permit fast diffusionof the reversed bias magnetic field. If turned on at t<−2 ms, the plasmastreams could fill the about 1 to 3 m³ field line volume of theformation and confinement regions of the formation sections 200 andconfinement chamber 100 with a target plasma density of a few 10¹³ cm⁻³,sufficient to allow neutral beam build-up prior to FRC arrival. Theformation FRCs could then be formed and translated into the resultingconfinement vessel plasma. In this way the plasma guns 350 enable a widevariety of operating conditions and parameter regimes.

Electrical Biasing

Control of the radial electric field profile in the edge layer 456 isbeneficial in various ways to FRC stability and confinement. By virtueof the innovative biasing components deployed in the FRC system 10 it ispossible to apply a variety of deliberate distributions of electricpotentials to a group of open flux surfaces throughout the machine fromareas well outside the central confinement region in the confinementchamber 100. In this way radial electric fields can be generated acrossthe edge layer 456 just outside of the FRC 450. These radial electricfields then modify the azimuthal rotation of the edge layer 456 andeffect its confinement via E×B velocity shear. Any differential rotationbetween the edge layer 456 and the FRC core 453 can then be transmittedto the inside of the FRC plasma by shear. As a result, controlling theedge layer 456 directly impacts the FRC core 453. Furthermore, since thefree energy in the plasma rotation can also be responsible forinstabilities, this technique provides a direct means to control theonset and growth of instabilities. In the FRC system 10, appropriateedge biasing provides an effective control of open field line transportand rotation as well as FRC core rotation. The location and shape of thevarious provided electrodes 900, 905, 910 and 920 allows for control ofdifferent groups of flux surfaces 455 and at different and independentpotentials. In this way a wide array of different electric fieldconfigurations and strengths can be realized, each with differentcharacteristic impact on plasma performance.

A key advantage of all these innovative biasing techniques is the factthat core and edge plasma behavior can be affected from well outside theFRC plasma, i.e. there is no need to bring any physical components intouch with the central hot plasma (which would have severe implicationsfor energy, flux and particle losses). This has a major beneficialimpact on performance and all potential applications of the HPF concept.

Experimental Data—HPF Operation

Injection of fast particles via beams from the neutral beam guns 600plays an important role in enabling the HPF regime. FIGS. 16A, 16B, 16C,and 16D illustrates this fact. Depicted is a set of curves showing howthe FRC lifetime correlates with the length of the beam pulses. Allother operating conditions are held constant for all dischargescomprising this study. The data is averaged over many shots and,therefore, represents typical behavior. It is clearly evident thatlonger beam duration produces longer lived FRCs. Looking at thisevidence as well as other diagnostics during this study, it demonstratesthat beams increase stability and reduce losses. The correlation betweenbeam pulse length and FRC lifetime is not perfect as beam trappingbecomes inefficient below a certain plasma size, i.e., as the FRC 450shrinks in physical size not all of the injected beams are interceptedand trapped. Shrinkage of the FRC is primarily due to the fact that netenergy loss (˜4 MW) from the FRC plasma during the discharge is somewhatlarger than the total power fed into the FRC via the neutral beams (˜2.5MW) for the particular experimental setup. Locating the beams at alocation closer to the mid-plane of the vessel 100 would tend to reducethese losses and extend FRC lifetime.

FIGS. 17A, 17B, 17C, and 17D illustrate the effects of differentcomponents to achieve the HPF regime. It shows a family of typicalcurves depicting the lifetime of the FRC 450 as a function of time. Inall cases a constant, modest amount of beam power (about 2.5 MW) isinjected for the full duration of each discharge. Each curve isrepresentative of a different combination of components. For example,operating the FRC system 10 without any mirror plugs 440, plasma guns350 or gettering from the gettering systems 800 results in rapid onsetof rotational instability and loss of the FRC topology. Adding only themirror plugs 440 delays the onset of instabilities and increasesconfinement. Utilizing the combination of mirror plugs 440 and a plasmagun 350 further reduces instabilities and increases FRC lifetime.Finally adding gettering (Ti in this case) on top of the gun 350 andplugs 440 yields the best results—the resultant FRC is free ofinstabilities and exhibits the longest lifetime. It is clear from thisexperimental demonstration that the full combination of componentsproduces the best effect and provides the beams with the best targetconditions.

As shown in FIG. 1, the newly discovered HPF regime exhibitsdramatically improved transport behavior. FIG. 1 illustrates the changein particle confinement time in the FRC system 10 between theconventionally regime and the HPF regime. As can be seen, it hasimproved by well over a factor of 5 in the HPF regime. In addition, FIG.1 details the particle confinement time in the FRC system 10 relative tothe particle confinement time in prior conventional FRC experiments.With regards to these other machines, the HPF regime of the FRC system10 has improved confinement by a factor of between 5 and close to 20.Finally and most importantly, the nature of the confinement scaling ofthe FRC system 10 in the HPF regime is dramatically different from allprior measurements. Before the establishment of the HPF regime in theFRC system 10, various empirical scaling laws were derived from data topredict confinement times in prior FRC experiments. All those scalingrules depend mostly on the ratio R²/ρ_(i), where R is the radius of themagnetic field null (a loose measure of the physical scale of themachine) and ρ_(i) is the ion larmor radius evaluated in the externallyapplied field (a loose measure of the applied magnetic field). It isclear from FIG. 1 that long confinement in conventional FRCs is onlypossible at large machine size and/or high magnetic field. Operating theFRC system 10 in the conventional FRC regime CR tends to follow thosescaling rules, as indicated in FIG. 1. However, the HPF regime is vastlysuperior and shows that much better confinement is attainable withoutlarge machine size or high magnetic fields. More importantly, it is alsoclear from FIG. 1 that the HPF regime results in improved confinementtime with reduced plasma size as compared to the CR regime. Similartrends are also visible for flux and energy confinement times, asdescribed below, which have increased by over a factor of 3-8 in the FRCsystem 10 as well. The breakthrough of the HPF regime, therefore,enables the use of modest beam power, lower magnetic fields and smallersize to sustain and maintain FRC equilibria in the FRC system 10 andfuture higher energy machines. Hand-in-hand with these improvementscomes lower operating and construction costs as well as reducedengineering complexity.

For further comparison, FIGS. 18A, 18B, 18C, and 18D shows data from arepresentative HPF regime discharge in the FRC system 10 as a functionof time. FIG. 18A depicts the excluded flux radius at the mid-plane. Forthese longer timescales the conducting steel wall is no longer as good aflux conserver and the magnetic probes internal to the wall areaugmented with probes outside the wall to properly account for magneticflux diffusion through the steel. Compared to typical performance in theconventional regime CR, as shown in FIGS. 13A, 13B, 13C, and 13D, theHPF regime operating mode exhibits over 400% longer lifetime.

A representative cord of the line integrated density trace is shown inFIG. 18B with its Abel inverted complement, the density contours, inFIG. 18C. Compared to the conventional FRC regime CR, as shown in FIGS.13A, 13B, 13C, and 13D, the plasma is more quiescent throughout thepulse, indicative of very stable operation. The peak density is alsoslightly lower in HPF shots—this is a consequence of the hotter totalplasma temperature (up to a factor of 2) as shown in FIG. 18D.

For the respective discharge illustrated in FIGS. 18A, 18B, 18C, and18D, the energy, particle and flux confinement times are 0.5 ms, 1 msand 1 ms, respectively. At a reference time of 1 ms into the discharge,the stored plasma energy is 2 kJ while the losses are about 4 MW, makingthis target very suitable for neutral beam sustainment.

FIG. 19 summarizes all advantages of the HPF regime in the form of anewly established experimental HPF flux confinement scaling. As can beseen in FIG. 19, based on measurements taken before and after t=0.5 ms,i.e., t≤0.5 ms and t>0.5 ms, the confinement scales with roughly thesquare of the electron Temperature. This strong scaling with a positivepower of T_(e) (and not a negative power) is completely opposite to thatexhibited by conventional tokomaks, where confinement is typicallyinversely proportional to some power of the electron temperature. Themanifestation of this scaling is a direct consequence of the HPF stateand the large orbit (i.e. orbits on the scale of the FRC topology and/orat least the characteristic magnetic field gradient length scale) ionpopulation. Fundamentally, this new scaling substantially favors highoperating temperatures and enables relatively modest sized reactors.

While the invention is susceptible to various modifications, andalternative forms, specific examples thereof have been shown in thedrawings and are herein described in detail. It should be understood,however, that the invention is not to be limited to the particular formsor methods disclosed, but to the contrary, the invention is to cover allmodifications, equivalents and alternatives falling within the spiritand scope of the appended claims.

In the description above, for purposes of explanation only, specificnomenclature is set forth to provide a thorough understanding of thepresent disclosure. However, it will be apparent to one skilled in theart that these specific details are not required to practice theteachings of the present disclosure.

The various features of the representative examples and the dependentclaims may be combined in ways that are not specifically and explicitlyenumerated in order to provide additional useful embodiments of thepresent teachings. It is also expressly noted that all value ranges orindications of groups of entities disclose every possible intermediatevalue or intermediate entity for the purpose of original disclosure, aswell as for the purpose of restricting the claimed subject matter.

Systems and methods for generating and maintaining an HPF regime FRChave been disclosed. It is understood that the embodiments describedherein are for the purpose of elucidation and should not be consideredlimiting the subject matter of the disclosure. Various modifications,uses, substitutions, combinations, improvements, methods of productionswithout departing from the scope or spirit of the present inventionwould be evident to a person skilled in the art. For example, the readeris to understand that the specific ordering and combination of processactions described herein is merely illustrative, unless otherwisestated, and the invention can be performed using different or additionalprocess actions, or a different combination or ordering of processactions. As another example, each feature of one embodiment can be mixedand matched with other features shown in other embodiments. Features andprocesses known to those of ordinary skill may similarly be incorporatedas desired. Additionally and obviously, features may be added orsubtracted as desired. Accordingly, the invention is not to berestricted except in light of the attached claims and their equivalents.

What is claimed is:
 1. A method for generating and maintaining amagnetic field with a field reversed configuration (FRC) comprisinggenerating a magnetic field with a magnetic system coupled to aconfinement chamber, first and second diametrically opposed FRCformation sections coupled to the confinement chamber, and first andsecond divertors coupled to the first and second formation sections, themagnetic system including first and second mirror plugs positionedbetween the first and second formation sections and the first and seconddivertors and two or more saddle coils coupled to the confinementchamber, gettering the confinement chamber and the first and seconddivertors with a layer of gettering material from a gettering systemcoupled to the confinement chamber and the first and second divertors,generating an FRC in each of the first and second formation sections andtranslating each FRC toward a midplane of the confinement chamber wherethe FRCs merge into a merged FRC, the first and second formationsections comprising a modularized formation system, injecting neutralatom beams into the merged FRC from a plurality of neutral atom beaminjectors coupled to the confinement chamber and oriented normal to theaxis of the confinement chamber, injecting plasma into the merged FRCfrom first and second axial plasma guns operably coupled to the firstand second divertors, the first and second formation sections and theconfinement chamber, and electrically biasing open flux surfaces of themerged FRC with one or more biasing electrodes being positioned withinone or more of the confinement chamber, the first and second formationsections, and the first and second divertors.
 2. The method of claim 1further comprising confining particles in the merged FRC for a period oftime that is greater by at least a factor of two (2) deviations than theparticle confinement time of an FRC having substantially the same radiusof a magnetic field null (R) and particle confinement scaling thatsubstantially depends on the ratio R²/ρ_(i), where ρ_(i) is an ion lamorradius evaluated in an externally applied field.
 3. The method of claim1 wherein the magnetic system includes a plurality of quasi-dc coilsaxially spaced in positions along the confinement chamber, the first andsecond formation sections, and the first and second divertors.
 4. Themethod of claim 3 wherein the magnetic system further comprises a firstset of mirror coils positioned between the ends of the confinementchamber and the first and second formation sections.
 5. The method ofclaim 4 wherein the mirror plug comprises a second set of mirror coilsbetween each of the first and second formation sections and the firstand second divertors.
 6. The method of claim 5 wherein the mirror plugfurther comprises a set of mirror plug coils wrapped around aconstriction in the passageway between each of the first and secondformation sections and the first and second divertors.
 7. The method ofclaim 1 wherein the mirror plug coils are compact pulsed mirror coils.8. The method of claim 1 wherein the first and second formation sectionscomprises an elongate tube.
 9. The method of claim 8 wherein theformation systems are pulsed power formation systems.
 10. The method ofclaim 8 wherein the step of forming and translating the FRCs includesenergizing a set of coils of individual ones of a plurality of strapassemblies wrapped around the elongate tube of the first and secondformation sections, wherein the formation systems comprise a pluralityof power and control units coupled to individual ones of the pluralityof strap assemblies.
 11. The method of claim 10 wherein individual onesof the plurality of power and control units comprising a trigger andcontrol system.
 12. The method of claim 11 wherein the trigger andcontrol systems of the individual ones of the plurality of power andcontrol units being synchronizable to enable static FRC formationwherein the FRC is formed and then injected or dynamic FRC formationwherein the FRC is formed and translated simultaneously.
 13. The methodof claim 1 wherein the plurality of neutral atom beam injectorscomprises one or more RF plasma source neutral atom beam injectors andone or more arc source neutral atom beam injectors.
 14. The method ofclaim 1 wherein the gettering system comprises one or more of a Titaniumdeposition system and a Lithium deposition system that coat the plasmafacing surfaces of the confine chamber and the first and seconddivertors.
 15. The method of claim 1 wherein biasing electrodes includesone or more of one or more point electrodes positioned within thecontainment chamber to contact open field lines, a set of annularelectrodes between the confinement chamber and the first and secondformation sections to charge far-edge flux layers in an azimuthallysymmetric fashion, a plurality of concentric stacked electrodespositioned in the first and second divertors to charge multipleconcentric flux layers, and anodes of the plasma guns to intercept openflux.
 16. A method for generating and maintaining a magnetic field witha field reversed configuration (FRC) comprising generating magneticfield with a magnetic system coupled to a confinement chamber, andsecond diametrically opposed FRC formation sections coupled to theconfinement chamber, and first and second divertors coupled to the firstand second formation sections, generating an FRC in each of the firstand second formation sections and translating each FRC toward a midplaneof the confinement chamber where the FRCs merge into a merged FRC,injecting neutral atom beams into the merged FRC from a plurality ofneutral atom beam injectors coupled to the confinement chamber andoriented normal to the axis of the confinement chamber, and injectingplasma into the merged FRC from first and second axial plasma gunsoperably coupled to the first and second divertors, the first and secondformation sections and the confinement chamber.
 17. The method of claim16 further comprising confining particles in the merged FRC for a periodof time that is greater by at least a factor of two (2) deviations thanthe particle confinement time of an FRC having substantially the sameradius of a magnetic field null (R) and particle confinement scalingthat substantially depends on the ratio R²/pi, where pi is an ion lamorradius evaluated in an externally applied field.
 18. The method of claim16 wherein the magnetic system includes a plurality of quasi-dc coilsaxially spaced in positions along the confinement chamber, the first andsecond formation sections, and the first and second divertors.
 19. Themethod of claim 18 wherein the magnetic system further comprises a firstset of mirror coils positioned between the ends of the confinementchamber and the first and second formation sections.
 20. The method ofclaim 19 wherein the mirror plug comprises a second set of mirror coilsbetween each of the first and second formation sections and the firstand second divertors.
 21. The method of claim 20 wherein the mirror plugfurther comprises a set of mirror plug coils wrapped around aconstriction in the passageway between each of the first and secondformation sections and the first and second divertors.
 22. The method ofclaim 21 wherein the mirror plug coils are compact pulsed mirror coils.23. The method of claim 22 further comprising injecting plasma into themerged FRC from first and second axial plasma guns operably coupled tothe first and second divertors, the first and second formation sectionsand the confinement chamber.
 24. The method of claim 22 furthercomprising gettering the confinement chamber and the first and seconddivertors with a layer of gettering material from a gettering systemcoupled to the confinement chamber and the first and second divertors.25. The method of claim 22 further comprising electrically biasing openflux surfaces of the merged FRC with one or more biasing electrodesbeing positioned within one or more of the confinement chamber, thefirst and second formation sections, and the first and second divertors.26. The method of claim 22 the magnetic system further comprising two ormore saddle coils coupled to the confinement chamber.
 27. The method ofclaim 22 further comprising injecting ion pellets into the merged FRCfrom an ion pellet injector coupled to the confinement chamber.
 28. Themethod of claim 22 wherein the formation section comprises modularizedformation systems for generating an FRC and translating it toward amidplane of the confinement chamber.